Question

1 Find the impulse response of H(z), where H(z) is the system 1-2+2 function of the difference equation of the 2nd-order IIR filter given by the block diagram Y(z) X(z) + X + +

Answer 1

290 flnswer:- Given data:- H(z ] - Eqh 1-52 + + 72 Now we have to find the implels responce of HCZ). hon the given blocks diagram. oond the differenticel Equation of the and order ur filter Givendiagram was: - x(2) + TO (2) 0 0 L z 7 Now we have to find Implelse Les pohons q HOZ) + Given Equation is ved ] - >> Hz) : - 622-52'*: 622 52 41 ? H[2] = 622 62²-52741 67 Here the Equation is H[2]= 4[2] 622 622 524

6d Now we can find Impulse Risponee of H[2] » X(2) = f x(n) = f(n) = Y(2) sett! ei + 52"-1 672524+1 = it 5211 [377-1][227-1] Factorize the above Equation. then we get then we get 5zti - [321][2240 (240 * 5244 = A (27_] + B [3371_1] Now we have fo Substitute | 2765 == (2x3 - 11 +(3x++) = 5**+ ! 17 :

pg » BX / 2 = 2 / 2 » Bx t = 3 * ☆ Now we have to stubstitute. 12+ = 1 / 1 = A (2%-1] +Bf3x3-- 5457 >> A[ 3-13 , 6x5- +2=2+43 A = -2 Then we can write y(2): 1+ 37t, +22 To get Impuls Response of f(23 we have to consider inverse 2- transform of 4C2) > yon)Sen) +2.3"ucn) -3.2?uin) and we can also write, as below Tyon)+6[31'den) -,4 uch)]] The giver Case is sowed 0_ * -o